My lips, nose, and cheeks have been numb for a full day- what could be causing this?

Need evaluation. You should see a doctor or go to the er if the symptoms are severe or associated with headache, change in vision, loss of sensation or weakness in other parts of the body. Sensation from the face is transmitted through branches of the trigeminal nerve, the fifth cranial nerve. Possible causes include metabolic like low calcium (typically causes numbness around the mouth), brain tumor and stroke.
Cranial nerve . Compression, especially the trigeminal nerve needs to be ruled out if your numbness is spontaneous as opposed to induced by a recent local anesthetic injection.